In [5]:
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
In [3]:
class Perceptron(object):
"""Perceptron classifier.
Parameters
------------
eta : float
Learning rate (between 0.0 and 1.0)
n_iter : int
Passes over the training dataset.
Attributes
-----------
w_ : 1d-array
Weights after fitting.
errors_ : list
Number of misclassifications in every epoch.
"""
def __init__(self, eta=0.01, n_iter=10):
self.eta = eta
self.n_iter = n_iter
def fit(self, X, y):
""" Fit training data.
Parameters
----------
X : {array-like}, shape = [n_samples, n_features]
Training vectors, where n_samples
is the number of samples and n_features is the number of features.
y : array-like, shape = [n_samples]
Target values.
Returns
-------
self : object
"""
self.w_ = np.zeros(1 + X.shape[1])
self.errors_ = []
for _ in range(self.n_iter):
errors = 0
for xi, target in zip(X, y):
update = self.eta * (target - self.predict(xi))
self.w_[1:] += update * xi
self.w_[0] += update
errors += int(update != 0.0)
self.errors_.append(errors)
return self
def net_input(self, X):
""" Calculate net input. """
return np.dot(X, self.w_[1:]) + self.w_[0]
def predict(self, X):
""" Return class label after unit step"""
return np.where(self.net_input(X) >= 0.0, 1, -1)
In [4]:
df = pd.read_csv('https://archive.ics.uci.edu/ml/machine-learning-databases/iris/iris.data', header=None)
df.tail()
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In [6]:
y = df.iloc[0:100, 4].values
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y = np.where(y == 'Iris-setosa', -1, 1)
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X = df.iloc[0:100, [0,2]].values
In [9]:
plt.scatter(X[:50, 0], X[:50,1], color='red', marker='o', label='setosa')
plt.scatter(X[50:100, 0], X[50:100,1], color='blue', marker='x', label='versicolor')
plt.xlabel('sepal length')
plt.ylabel('petal length')
plt.legend(loc='upper left')
plt.show()
In [10]:
ppn = Perceptron(eta=0.1, n_iter=10)
ppn.fit(X, y)
plt.plot(range(1, len(ppn.errors_) + 1), ppn.errors_, marker='o')
plt.xlabel('Epochs')
plt.ylabel('Number misclassications')
plt.show()
In [11]:
from matplotlib.colors import ListedColormap
In [14]:
def plot_decision_regions(X, y, classifier, resolution=0.02):
#setup marker generator and color map
markers = ('s','x','o','^','v')
colors = ('red','blue','lightgreen','gray','cyan')
cmap = ListedColormap(colors[:len(np.unique(y))])
#plot the decision surface
x1_min, x1_max = X[:,0].min() - 1, X[:,0].max() + 1
x2_min, x2_max = X[:,1].min() - 1, X[:,1].max() + 1
xx1, xx2 = np.meshgrid(np.arange(x1_min, x1_max, resolution),
np.arange(x2_min, x2_max, resolution))
Z = classifier.predict(np.array([xx1.ravel(), xx2.ravel()]).T)
Z = Z.reshape(xx1.shape)
plt.contourf(xx1, xx2, Z, alpha=0.4, cmap=cmap)
plt.xlim(xx1.min(), xx1.max())
plt.ylim(xx2.min(), xx2.max())
#plot class samples
for idx, c1 in enumerate(np.unique(y)):
plt.scatter(x=X[y == c1, 0], y=X[y == c1, 1],
alpha = 0.8, c=cmap(idx), marker=markers[idx], label=c1)
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plot_decision_regions(X, y, classifier=ppn)
plt.xlabel('sepal length [cm]')
plt.ylabel('petal length [cm]')
plt.legend(loc='upper left')
plt.show()
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class AdalineGD(object):
"""ADAptive LInear NEuron classifier Gradient Descent
Parameters
------------
eta : float
Learning rate (between 0.0 and 1.0)
n_iter : int
Passes over the training dataset.
Attributes
-----------
w_ : 1d-array
Weights after fitting.
errors_ : list
Number of misclassifications in every epoch.
"""
def __init__(self, eta=0.01, n_iter=50):
self.eta = eta
self.n_iter = n_iter
def fit(self, X, y):
""" Fit training data.
Parameters
----------
X : {array-like}, shape = [n_samples, n_features]
Training vectors,
where n_samples is the number of samples and
n_features is the number of features.
y : array-like, shape = [n_samples]
Target values.
Returns
-------
self : object
"""
self.w_ = np.zeros(1 + X.shape[1])
self.cost_ =[]
for i in range(self.n_iter):
output = self.net_input(X)
errors = (y - output)
self.w_[1:] += self.eta * X.T.dot(errors)
self.w_[0] += self.eta * errors.sum()
cost = (errors**2).sum() / 2.0
self.cost_.append(cost)
return self
def net_input(self,X):
"""Calculate net input."""
return np.dot(X, self.w_[1:]) + self.w_[0]
def activation(self,X):
""" Compute linear activation """
return self.net_input(X)
def predict(self, X):
"""Return class label after unit step"""
return np.where(self.activation(X) >= 0.0, 1, -1)
In [21]:
fig, ax = plt.subplots(nrows=1, ncols=2, figsize=(8,4))
ada1 = AdalineGD(n_iter=10, eta=0.01).fit(X,y)
ax[0].plot(range(1, len(ada1.cost_) + 1), np.log10(ada1.cost_), marker='o')
ax[0].set_xlabel('Epochs')
ax[0].set_ylabel('log(Sum-squared-error)')
ax[0].set_title('Adaline - learning rate 0.01')
ada2 = AdalineGD(n_iter=10, eta = 0.0001).fit(X,y)
ax[1].plot(range(1, len(ada2.cost_)+1), ada2.cost_, marker='o')
ax[1].set_xlabel('Epochs')
ax[1].set_ylabel('Sum-squared-error')
ax[1].set_title('Adaline - learning rate 0.0001')
plt.show()
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X_std = np.copy(X)
X_std[:,0] = (X[:,0] - X[:,0].mean()) / X[:,0].std()
X_std[:,1] = (X[:,1] - X[:,1].mean()) / X[:,1].std()
In [24]:
ada = AdalineGD(n_iter=15, eta=0.01)
ada.fit(X_std, y)
plot_decision_regions(X_std, y, classifier=ada)
plt.title('Adaline - Gradient Descent')
plt.xlabel('sepal length [standardized]')
plt.ylabel('petal length [standardized]')
plt.legend(loc='upper left')
plt.show()
plt.plot(range(1, len(ada.cost_) + 1), ada.cost_, marker='o')
plt.xlabel('Epochs')
plt.ylabel('sum-squared-error')
plt.show()
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from numpy.random import seed
class AdalineSGD(object):
"""ADAptive LInear NEuron classifier Stochastic Gradient Descent
Parameters
------------
eta : float
Learning rate (between 0.0 and 1.0)
n_iter : int
Passes over the training dataset.
Attributes
-----------
w_ : 1d-array
Weights after fitting.
errors_ : list
Number of misclassifications in every epoch.
shuffle : bool (default: True)
Shuffles training data every epoch
if True to prevent cycles.
random_state : int (default: None)
Set random state for shuffling
and initializing the weights.
"""
def __init__(self, eta=0.01, n_iter=10, shuffle=True, random_state=None):
self.eta = eta
self.n_iter = n_iter
self.w_initialized = False
self.shuffle = shuffle
if random_state:
seed(random_state)
def fit(self, X, y):
""" Fit training data.
Parameters
----------
X : {array-like}, shape = [n_samples, n_features]
Training vectors,
where n_samples is the number of samples and
n_features is the number of features.
y : array-like, shape = [n_samples]
Target values.
Returns
-------
self : object
"""
self._initialize_weights(X.shape[1])
self.cost_ =[]
for i in range(self.n_iter):
if self.shuffle:
X, y = self._shuffle(X,y)
cost = []
for xi, target in zip(X, y):
cost.append(self._update_weights(xi, target))
avg_cost = sum(cost)/len(y)
self.cost_.append(avg_cost)
return self
def partial_fit(self, X, y):
"""Fit training data without reinitializing the weights"""
if not self.w_initialized:
self._initialize_weights(X.shape[1])
if y.ravel().shape[0] > 1:
for xi, target in zip(X, y):
self._update_weights(xi, target)
else:
self._update_weights(X, y)
return self
def _shuffle(self, X, y):
""" Shuffle training data"""
r = np.random.permutation(len(y))
return X[r], y[r]
def _initialize_weights(self, m):
"""Initialize weights to zeros"""
self.w_ = np.zeros(1 + m)
self.w_initialized = True
def _update_weights(self, xi, target):
"""Apply Adaline learning rule to update the weights"""
output = self.net_input(xi)
error = (target - output)
self.w_[1:] += self.eta * xi.dot(error)
self.w_[0] += self.eta * error
cost = 0.5 * error**2
return cost
def net_input(self,X):
"""Calculate net input."""
return np.dot(X, self.w_[1:]) + self.w_[0]
def activation(self,X):
""" Compute linear activation """
return self.net_input(X)
def predict(self, X):
"""Return class label after unit step"""
return np.where(self.activation(X) >= 0.0, 1, -1)
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ada = AdalineSGD(n_iter=15, eta=0.01, random_state=1)
ada.fit(X_std, y)
plot_decision_regions(X_std, y, classifier=ada)
plt.title('Adaline - stochastic gradient descent')
plt.xlabel('sepal length [standardized]')
plt.ylabel('petal length [standardized]')
plt.legend(loc='upper left')
plt.show()
plt.plot(range(1, len(ada.cost_) + 1), ada.cost_, marker='o')
plt.xlabel('Epochs')
plt.ylabel('Average cost')
plt.show()
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